Tidiane Cheik Diaw, 27, from Senegal, was accused of strangling to death Miss Olsen, 35, a well-liked event organiser who documented her idyllic life in Tuscany with dozens of photographs on her Instagram account.

The arrest of an immigrant for the high-profile murder, which evoked comparisons with the killing of British student Meredith Kercher in Perugia in 2007, is likely to fuel the debate in Europe over crime and immigration, particularly in the wake of the mass sexual assaults in Cologne and other cities on New Year’s Eve.

More than 150,000 migrants, refugees and asylum seekers reached Italy’s shores by boat from Libya last year, the vast majority of them young men.

Of Italy’s total prison population of 52,000, a third are foreigners.

Miss Olsen’s naked body was found in her flat in Florence on Saturday by her Italian boyfriend, who was left distraught by the discovery.

Diaw is believed to have arrived illegally in Italy several months ago in order to join his brother and was eking out a living in Florence by distributing nightclub flyers.

Diaw Cheikh Tidiane, suspect in the death of an American woman Photo: Italian Police/EPA

Investigators believe Miss Olsen met him in the early hours of the morning last Friday after leaving a nightclub, the Montecarla.

The pair walked back to her flat in Via Santa Monica and had consensual sex, possibly under the influence of drugs and alcohol.

But a furious argument developed after Miss Olsen told him he had to leave the apartment because her Italian boyfriend was about to arrive.

She sustained two fractures to her skull and is believed to have died at around 8am on Friday morning, prosecutors said.

Diaw allegedly told police that he pushed her to the ground, where she hit her head hard, but said that he had not meant to kill her.

He was identified from security camera footage which showed him walking with Miss Olsen from the club to her flat, and by DNA evidence.

Ashley Olsen with her beagle, Scout Photo: Instagram

Police first began to consider him as a suspect earlier this week and pulled him in for questioning.

In the course of the interrogation, officers offered him a cigarette. After he discarded it they retrieved the butt and recovered DNA from it.

They then matched that with DNA found on a condom and a cigarette butt that were found in Miss Olsen’s flat, as well as genetic material found beneath her finger nails.

He also stole her mobile phone and put his own SIM card inside it, investigators said.

Giuseppe Creazzo, the chief prosecutor in the case, said investigators had found “very serious indications of his guilt”.

The suspect had "substantially admitted" being responsible for the killing, Mr Creazzo said.

Miss Olsen’s body, naked apart from a pair of socks, was found in her flat on Saturday by her Italian boyfriend, Federico Fiorentini, a 43-year-old artist.

He had become concerned that he had not heard from her for a few days, after the couple had an argument.

Diaw, who is being held in prison, faces a charge of murder aggravated by cruelty.

The route from the nightclub to Ms Olsen's street

Miss Olsen, originally from Florida, had been living in Florence for three years, working for a British event management firm.

She was rebuilding her life after the trauma of a divorce in the US.

She had also moved to Italy to be close to her father, Walter Olsen, an architect who teaches at a local art college.

In a statement released earlier this week, her best friend, Jade Moss, said she had been left “bereft and numbed” by the killing.

Miss Moss, the founder and creative director of the London-based event management company, Monday’s Child, called the murder “horrific and unimaginable.”

The statement, written by her on behalf of all Miss Olsen’s close friends in Florence, said: “Ashley was a rare and kind-hearted spirit. She immediately became a familiar part of life in the Oltrarno (district of Florence) where she lived, embraced by everyone who knew her.

Ashley Olsen had been living in the Italian city of Florence Photo: Instagram

Ashley’s beloved dog, Scout, and her quirky style marked her out. From a distance she stood out, you saw her coming. Up close it was the warm and vivacious smile that lit up her whole face that we, and so many others, will remember her by.”

Miss Olsen worked for the UK-based company at its branch in Florence, organising events in Italy.

The company’s website describes her as “a very creative soul with a flair and talent for anything visually unique and eclectic.”

Miss Olsen’s mother and sister flew into Florence on Thursday.

Her funeral will be held on Friday at the Basilica of Santo Spirito, close to where she lived.